The purpose of this note is to introduce a new functional of the domain, to be used in shape optimization problems as a means to enforce the constructibility of shapes by additive manufacturing processes. This functional aggregates the self-weights of all the intermediate structures of the shape appearing in the course of its layer by layer assembly. Its mathematical analysis is outlined and an algorithm is proposed to accelerate the significant computational effort entailed by the implementation of these ideas. Eventually, a numerical validation and a concrete example are discussed.